Closed Surfaces and Integrals

Related lectures (32)

Page 2 of 4

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Covers the calculation of angles between curves on regular surfaces and the concept of curvilinear abscissa.

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Explores orientable surfaces, scalar field integrals, and practical applications through examples with a sphere and a cone.

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.